An integrated yield-line approach to tensile and compressive membrane actions in thin lightly-reinforced concrete slabs

In this paper a recently developed method of analysis is used to examine the effects of rotational and normal continuity at parallel edges on the large-deflection behaviour of lightly reinforced rectangular concrete slabs. The method makes the conventional assumption of an optimal yield-line mechanism at infinitesimal deflection, and subsequently ensures equilibrium of the flat facets of the mechanism using the correct kinematics as the deflection increases. For slabs which are only supported transversely at their edges the method was developed to model the development of tensile membrane action, which enhances the slab’s load capacity as its deflection increases, This has particular practical applications in the resistance of buildings to hazard loads, particularly fire. The fracture ductility of reinforcing mesh crossing yield lines is used to monitor the progressive fracture of the mesh across the yield-line cracks. This progressive fracture causes the enhancement of load capacity to have natural limits, depending largely on the bond characteristics of the bars at a discrete crack-face.

When rotational continuity at parallel edges is modelled as an extension to the technique, by forcing plastic hinges to develop along these edges as part of the yield-line mechanism, this enhances the yield-line failure load of the slab, but has no effect on either the geometry of the yield line or the additional load capacity at any value of deflection. However, if these edges are assumed also to be fully restrained so that there can be no outward movement of the slab, the initial yield-line mechanism is immediately subject to compressive membrane action. This can generate a very high initial load capacity, which rapidly declines as the deflection increases, but may subsequently rise slowly as tensile membrane action develops. However, it is essential in all cases that reinforcement has high ductility across yield lines if any significantly rising load capacity is to be generated as the deflection rises.